3 June - Fixed Income

FIXED-INCOME PORTFOLIO MEASURES

Learning Outcome

• describe fixed-income portfolio measures of risk and return as well as correlation characteristics

We first provide a brief review of fixed-income risk and return measures introduced in earlier lessons (Exhibit 8).

Exhibit 8:

Bond Risk and Return Measures

Macaulay duration (MacDur)	Macaulay duration is a weighted average of the time to receipt of the bond’s promised payments, where the weights are the shares of the full price that correspond to each of the bond’s promised future payments.
Modified duration (ModDur)	The Macaulay duration statistic divided by one plus the yield per period, which estimates the percentage price change (including accrued interest) for a bond given a change in its yield to maturity.
Effective duration (EffDur)	The sensitivity of the bond’s price to a change in a benchmark yield curve (i.e., using a parallel shift in the benchmark yield curve (ΔCurve). Effective duration is essential to the measurement of the interest rate risk of a complex bond where future cash flows are uncertain.
Key rate duration (KeyRatDur, also called partial duration)	A measure of a bond’s sensitivity to a change in the benchmark yield curve at a specific maturity point or segment. Key rate durations help identify “shaping risk” for a bond or a portfolio—that is, its sensitivity to changes in the shape of the benchmark yield curve (e.g., the yield curve becoming steeper or flatter or showing more or less curvature).
Empirical duration	A measure of interest rate sensitivity that is determined from market data—that is, run a regression of bond price returns on changes in a benchmark interest rate (for example, the price returns of a 10-year euro-denominated corporate bond could be regressed on changes in the 10-year German bund or the 10-year Euribor swap rate).
Money duration	A measure of the price change in units of the currency in which the bond is denominated. Money duration can be stated per 100 of par value or in terms of the bond’s actual position size in the portfolio. Commonly called “dollar duration” in the United States.
Price value of a basis point (PVBP)	An estimate of the change in a bond’s price given a 1 bp change in yield to maturity. PVBP “scales” money duration so that it can be interpreted as money gained or lost for each basis point change in the reference interest rate. Also referred to in North America as the “dollar value of an 0.01” (pronounced oh-one) and abbreviated as DV01. It is calibrated to a bond’s par value of 100; for example, a DV01 of $0.08 is equivalent to 8 cents per 100 points. (The terms PVBP and DV01 are used interchangeably; we will generally use PVBP, but DV01 has the same meaning). A related statistic to PVBP, sometimes called “basis point value” (or BPV), is the money duration times 0.0001 (1 bp).
Convexity	A second-order effect that describes a bond’s price behavior for larger yield movements. It captures the extent to which the yield/price relationship deviates from a linear relationship. If a bond has positive convexity, the expected return of the bond will be higher than the return of an identical-duration, lower-convexity bond if interest rates change. This price behavior is valuable to investors, and therefore, a bond with higher convexity might be expected to have a lower yield to maturity than a similar-duration bond with less convexity. Nominal convexity calculations assume that the cash flows do not change when yields to maturity change.
Effective convexity (EffCon)	A curve convexity statistic that measures the secondary effect of a change in a benchmark yield curve. A pricing model is used to determine the new prices when the benchmark curve is shifted upward (PV+) and downward (PV−) by the same amount (ΔCurve), holding other factors constant.

Exhibit 8 provides a reminder of convexity and why it is valuable. It is likely to be even more valuable when interest rate volatility is expected to increase.

This dynamic tends to drive changes in the shape of the yield curve: As convexity becomes more valuable, investors will bid up prices on the longer-maturity bonds (which have more convexity), and the long end of the curve may decline or even invert (or invert further), increasing the curvature of the yield curve.

A helpful heuristic for understanding convexity is that for zero-coupon (option free) bonds, the following are true:

• Macaulay durations increase linearly with maturity: A 30-year zero-coupon bond has three times the duration of a 10-year zero-coupon bond. Convexity is approximately proportional to duration squared; therefore, a 30-year zero-coupon bond has about nine times the convexity of a 10-year zero-coupon bond.

• Coupon-paying bonds have more convexity than zero-coupon bonds of the same duration: A 30-year coupon-paying bond with a duration of approximately 18 years has more convexity than an 18-year zero-coupon bond. The more widely dispersed a bond’s cash flows are around the duration point, the more convexity it will exhibit. For this reason, a zero-coupon bond has the lowest convexity of all bonds of a given duration.

Scaling Conventions

Convexity statistics must always be interpreted carefully because there is no convention for how they should be presented. When calculating the impact of convexity in approximating returns, the proper accounting for the scaling of convexity is important. Note that some data vendors report the convexity statistic divided by 100, whereas other applications may use the “raw” number.

Portfolio Measures of Risk and Return

Building on the measures of risk and return that apply to individual fixed-income securities, we now provide an overview of measures of risk and return applicable to portfolios of fixed-income securities. We will then illustrate their use in fixed income in a portfolio management scenario and refer to them in the subsequent coverage of liability-driven investing and total return strategies.

Bond portfolio duration is the sensitivity of a portfolio of bonds to small changes in interest rates. Recall that it can be calculated as the weighted average of time to receipt of the aggregate cash flows or, more commonly, as the weighted average of the individual bond durations of the portfolio.

Modified duration of a bond portfolio indicates the percentage change in the market value given a change in yield to maturity. If the modified duration of a portfolio is 15, then for a 100 bp increase or decrease in yield to maturity, the market value of the portfolio is expected to decrease or increase by about 15%. Modified duration of a portfolio comprising j fixed-income securities can be estimated as

where MV stands for market value of the portfolio and MVj is the market value of a specific bond.

Convexity of a bond portfolio can be a valuable tool when positioning a portfolio. Importantly, it is a second-order effect; it operates behind duration in importance and can largely be ignored for small yield changes. When convexity is added with the use of derivatives, however, it can be extremely important to returns. This effect will be demonstrated later. Negative convexity may also be an important factor in a bond’s or a portfolio’s returns. For bonds with short option positions embedded in their structures (such as mortgage-backed securities or callable bonds) or portfolios with short option positions, the convexity effect may be large. For a portfolio comprising j fixed-income securities, it can be estimated as

Adding convexity to a portfolio is not costless. Portfolios with higher convexity are most often characterized by lower yields to maturity.

Investors will be willing to pay for increased convexity when they expect yields to change by more than enough to cover the amount given up in yield to maturity.

Convexity is more valuable when yields to maturity are more volatile.

A portfolio’s convexity can be altered by shifting the maturity/duration distribution of bonds in the portfolio, by adding individual bonds with the desired convexity properties, or by using derivatives.

Effective duration and convexity of a portfolio are the relevant summary statistics when future cash flows of bonds in a portfolio are contingent on interest rate changes.

Spread duration is a useful measure for determining a portfolio’s sensitivity to changes in credit spreads.

Duration indicates the percentage price effect of an interest rate change on a bond, and spread duration measures the effect of a change in yield spread on a bond’s price.

Spread duration provides the approximate percentage increase (decrease) in bond price expected for a 1% decrease (increase) in credit spread.

Duration times spread (DTS) is a modification of the spread duration definition to incorporate the empirical observation that spread changes across the credit spectrum tend to occur on a proportional percentage basis rather than being based on absolute basis point changes.

This measure, reviewed in detail in a later lesson, weights the spread duration by a factor equal to the current credit spread, increasing the magnitude of expected price changes for a given change in spread.

Portfolio dispersion captures the variance of the times to receipt of cash flows with respect to the duration.

It is used in measuring interest rate immunization for liabilities.

Whereas Macaulay duration is the weighted average of the times to receipt of cash flows, dispersion is the weighted variance.

It measures the extent to which the payments are spread out around the duration.

Convexity is affected by the dispersion of cash flows. Higher cash flow dispersion leads to an increase in convexity.

Correlations between Fixed-Income Sectors

Correlation characteristics refer to the interplay between benchmark rates, spreads, and such factors as currencies.

Correlations between fixed-income sectors within a market are likely to be higher than those across markets given country-specific factors, such as central bank policy, economic growth, and inflation. In developed economies, investment-grade securities with a low probability of default are highly correlated with interest rate changes in the sovereign yield curve.

Below-investment-grade securities are affected more by changes in spread than by changes in general interest rates and often exhibit stronger correlations with equity markets.

Recall that correlations between interest rates and spreads can often be negative.

As the economy worsens, interest rates fall and spreads widen, and the reverse occurs when the economy improves.

Correlations for global government bonds will be partly driven by changes in interest rates but also by changes in local currency exchange rates.

Use of Measures of Risk and Return in Portfolio Management

We now provide an overview of how portfolio measures may be used by fund managers to reflect their views.

Portfolio Duration in Total Return Mandates

Total return mandates that are actively managed often use a top-down approach to establish the large risk factors in a portfolio combined with a bottom-up approach of individual security selection.

The analytics discussed earlier can be used to measure and manage the macroeconomic risk factors in the portfolio.

Portfolio managers develop or use a forecast of the direction of the economy and an assessment of the current business, political, and regulatory environment to develop themes that can be reflected in the portfolio.

On the basis of expectations for changes in interest rates and the shape of the yield curve, portfolio managers can adjust the duration of a portfolio to reflect their view.

For example, if the portfolio manager expects interest rates to rise and the yield curve to steepen, she would reduce the exposure of the portfolio to longer-dated bonds relative to the benchmark, which would reduce portfolio duration.

If her view materialized as expected, all else equal, the fund would outperform the benchmark, resulting in active excess returns.

Managing Credit Exposure Using Spread Duration

Portfolio managers often use the spread duration measures introduced earlier to gauge the portfolio’s sensitivity to changes in credit spreads.

A portfolio manager expecting credit spreads to narrow may wish to increase the spread duration in an actively managed portfolio.

The manager may face constraints, such as a target duration, rating-based restrictions, or limits to derivatives use, as part of the investment mandate.

A second way to increase the portfolio credit exposure is to reduce the average credit rating of the portfolio; for example, reduce A rated names and increase BBB rated credits.

In this case, the duration times spread measure may be a more appropriate measure of portfolio value changes. These active portfolio management tools are addressed in more detail in a later lesson on credit strategies.

The single bond risk and return measures discussed previously at an aggregate level will determine the large risk factors for the portfolio.

The portfolio manager will select securities as part of the portfolio construction process to achieve a targeted level of tracking error or active risk relative to a benchmark.

The contribution to duration, convexity, spread duration, and DTS of a single bond to the portfolio is weighted by the market value of the position relative to the total market value of the portfolio.

The portfolio manager will select a diversified universe of holdings to construct the portfolio in the manner he believes will optimize expected return and risk.

Relative Value Concept

Relative value is a key concept in the active management of fixed-income portfolios that describes the selection of the most attractive individual securities to populate the portfolio with, using ranking and comparing.

Portfolio managers analyze and rank securities on the basis of such considerations as valuation, issuer fundamentals, and market technical conditions (supply and demand).

This analysis is carried out across sectors, issuers, and individual securities to select securities with the most attractive risk and return profiles.

The portfolio manager will establish a time horizon over which the relative value analysis is applied.

The single bond characteristics can be used to express an active position relative to the benchmark.

For example, each bond has a distinct key rate duration (KeyRateDur) profile.

If the portfolio manager wants to establish a bullet or barbell position as part of the active risk decision, bonds with a specific KeyRateDur profile will be selected.

Similarly, the portfolio manager can select securities that in aggregate have more/less DTS than the benchmark if she is bullish/bearish on corporate bond spreads.

The selection of the most attractive individual securities to populate the portfolio will apply relative value analysis to compare and rank securities.

In the context of the efficient frontier, those securities that offer the most expected return for a given level of risk would offer the best relative value.

The positioning of the portfolio reflects the portfolio manager’s total return expectations for the market and relative returns versus the benchmark, given his views with regard to both the direction of interest rates and credit spread changes.

Diversification considerations ensure that idiosyncratic risks are within acceptable risk parameters.

EXAMPLE 3

1. Which of the following best describes a measure of sensitivity to changes in yields to maturity for a portfolio of bonds with cash flows contingent on interest rate changes?

   1. Portfolio dispersion

   2. Modified duration

   3. Effective duration

   Solution to 1:

   C is correct. Effective duration is particularly relevant in scenarios where the cash flows from the bonds held in a portfolio are contingent on changes in interest rates.

2. Which of the following is a true statement about portfolio dispersion?

   1. It can be described as the variance of time to the receipt of cash flows.

   2. The higher the dispersion, the lower the convexity of the portfolio.

   3. It determines the portfolio’s sensitivity to changes in credit spreads.

   Solution to 2:

   A is correct. Dispersion measures the variance of the time to receive cash flows from the fixed-income securities held.

BOND MARKET LIQUIDITY

Learning Outcome

• describe bond market liquidity, including the differences among market sub-sectors, and discuss the effect of liquidity on fixed-income portfolio management

A liquid security is one that may be transacted quickly with little effect on the security’s price.

Fixed-income securities vary greatly in their liquidity.

Compared with equities, fixed-income markets are generally less liquid.

The global fixed-income universe contains many individual bonds with varying features.

Many issuers have multiple bonds outstanding with their own unique maturity dates, coupon rates, early redemption features, and other specific features.

An important structural feature affecting liquidity is that fixed-income markets are typically over-the-counter dealer markets. Search costs (the costs of finding a willing counterparty) exist in bond markets because investors may have to locate desired bonds. In addition, when either buying or selling, investors may have to obtain quotes from various dealers to obtain the most advantageous pricing.

With limited, although improving, sources for transaction prices and quotes, bond markets are ordinarily less transparent than equity markets.

Liquidity, search costs, and price transparency are closely related to the type of issuer and its credit quality.

An investor is likely to find that bonds of a highly creditworthy government issuer are more liquid, have greater price transparency, and have lower search costs than bonds of, for example, a corporate issuer with lower credit quality.

Bond liquidity is typically highest immediately after issuance.

For example, an on-the-run bond issue (the most recently issued bonds) of a highly creditworthy sovereign entity is typically more liquid than a bond with similar features—including maturity—that was issued previously (an off-the-run bond).

On-the-run bonds also trade at narrow bid–ask spreads. This difference in liquidity is typically present even if the off-the-run bond was issued only one or two months earlier.

One reason for this phenomenon is that soon after bonds are issued, dealers normally have a supply of the bonds in inventory, but as time goes by and bonds are traded, many are purchased by buy-and-hold investors.

Once in the possession of such investors, those bonds are no longer available for trading.

Recall that liquidity typically affects bond yields to maturity.

Bond investors require higher yields for investing in illiquid securities relative to otherwise identical securities that are more liquid.

The higher yield to maturity compensates investors for the costs they may encounter if they try to sell illiquid bonds prior to maturity.

These costs include the opportunity costs associated with the delays in finding trading counterparties, as well as the bid–ask spread (which is a direct loss of wealth).

The incremental yield to maturity investors require for holding illiquid bonds instead of liquid bonds is referred to as a liquidity premium.

The magnitude of the liquidity premium normally varies depending on such factors as the issuer, the issue size, and time to maturity. For example, when a 10-year US Treasury bond shifts from on-the-run to off-the-run status, it typically trades at a yield to maturity several basis points above that of the new on-the-run bond.

Liquidity among Bond Market Sub-Sectors

Bond market liquidity varies across sub-sectors.

These sub-sectors can be categorized by such key features as issuer type, credit quality, issue size, and maturity.

The global bond market includes sovereign government bonds, non-sovereign government bonds, government-related bonds, corporate bonds, and securitized bonds (such as asset-backed securities and commercial mortgage-backed securities).

Sovereign government bonds are typically more liquid than corporate and non-sovereign government bonds. Their superior liquidity relates to their large issuance size, use as benchmark bonds, acceptance as collateral in the repo market, and well-recognized issuers.

Sovereign government bonds of countries with high credit quality and large issuance are typically more liquid than bonds of lower-credit-quality countries.

Corporate bonds are issued by many different companies and represent a wide spectrum of credit quality. For corporate bonds with low credit quality, it can be difficult to find a counterparty dealer with the securities in inventory or willing to take them into inventory.

Bonds of infrequent issuers are often less liquid than the bonds of issuers with many outstanding issues because market participants are less familiar with companies that seldom issue debt. In addition, smaller issues are generally less liquid than larger issues because small bond issues are typically excluded from major bond indexes with minimum issue size requirements.

The Effects of Liquidity on Fixed-Income Portfolio Management

Liquidity concerns influence fixed-income portfolio management in multiple ways, including pricing, portfolio construction, and consideration of alternatives to bonds (such as derivatives).

Pricing

Sources for pricing of recent bond transactions—notably corporate bonds—are not always readily available. Note that price transparency is improving in some bond markets. In the United States, the Financial Industry Regulatory Authority’s Trade Reporting and Compliance Engine (TRACE) and the Municipal Securities Rulemaking Board’s Electronic Municipal Market Access (EMMA) are electronic systems that help increase transparency in corporate and municipal bond markets, and similar initiatives play a similar role elsewhere for corporate bonds traded on market exchanges, increasing pricing transparency. In most bond markets, however, the lack of transparency in corporate bond trading presents a challenge.

Because many bonds do not trade or trade infrequently, using recent transaction prices to represent current value is not practical. Reliance on last traded prices, which may be out of date and may not incorporate current market conditions, could result in costly trading decisions. The determinants of corporate bond value, including interest rates, credit spreads, and liquidity premiums, change frequently. One solution to the pricing problem is to use matrix pricing that makes use of observable liquid benchmark yields of similar maturity and duration as well as benchmark spreads of bonds with comparable times to maturity, credit quality, and sector or security type to estimate the current market yield and price.

Portfolio Construction

Investors’ liquidity preferences directly influence portfolio construction. In constructing a portfolio, investors must consider the important trade-off between yield to maturity and liquidity. As mentioned previously, illiquid bonds typically have higher yields to maturity; a buy-and-hold investor seeking higher returns will often prefer less liquid bonds with higher yields to maturity. In contrast, investors who prefer greater liquidity will likely sacrifice returns and choose more liquid bonds with lower yields to maturity. Some investors may restrict their portfolio holdings to bonds within a certain maturity range. This restriction reduces the need to sell bonds to generate needed cash inflows. In such cases, the investors that anticipate their liquidity needs may give up the higher yield to maturity typically available to longer-term bonds. In addition to avoiding longer-term bonds, investors with liquidity concerns may also avoid small issues and private placements of corporate bonds.

A challenge in bond portfolio construction relates to the dealer market. Bond dealers often carry an inventory of bonds because buy and sell orders do not arrive simultaneously.

A dealer is not certain how long bonds will remain in its inventory. Less liquid bonds are likely to remain in inventory longer than liquid bonds.

A dealer provides bid–ask quotes (prices at which it will buy and sell) on bonds of its choice.

Some illiquid bonds will not have quotes, particularly bid quotes, from any dealer.

A number of different factors determine the bid–ask spread. Riskier bonds often have higher bid–ask spreads because of dealers’ aversion to hold those bonds in inventory. Because bond dealers must finance their inventories, the dealers incur costs in both obtaining funding and holding those bonds. Dealers seek to cover their costs and make a profit through the bid–ask spread, and therefore, the spread will be higher for illiquid bonds that are likely to remain in inventory longer.

A bond’s bid–ask spread is also a function of the bond’s complexity and how easily market participants can analyze the issuer’s creditworthiness. Bid–ask spreads in government bonds are generally lower than spreads in corporate bonds or structured financial instruments, such as asset-backed securities. Conventional (plain vanilla) corporate bonds normally have lower spreads than corporate bonds with non-standard or complex features, such as embedded options. Bonds of large, high-credit-quality corporations that have many outstanding bond issues are the most liquid among corporate bonds, and thus they have relatively low bid–ask spreads compared with smaller, less creditworthy companies.

Illiquidity directly increases bid–ask spreads of bonds, which increases the cost of trading. Higher transaction costs reduce the benefits of active portfolio decisions and may decrease portfolio managers’ willingness to adjust their portfolios to take advantage of opportunities that present themselves. As an example to quantify trading costs, if a corporate bond with a 15-year duration is being quoted by dealers with a 10 bp bid–ask spread, the cost impact to the portfolio is approximately 1.50% (0.0010 × 15 × 100 = 1.50%). The portfolio manager would buy the bond at $100, and when the portfolio is priced (typically at bid or the midpoint between the bid and the ask), the bond would have a value of $98.50, reducing total portfolio return. This is the price that would be realized if the bond were sold, holding other factors constant. To mitigate trading costs, investors can participate in the primary or new issue market where bonds are typically issued at a discount to the price at which a similar issue trades in the secondary market.

EXAMPLE 1

Knowledge Check

1. Rank the following instruments from the usually most liquid to the least liquid:

   • Low-credit-quality corporate bond

   • Recently issued on-the-run sovereign bond issued by a high-credit-quality government

   • High-credit-quality corporate bond

   • Sovereign bond issued a year ago by a high-credit-quality government

   Solution:

   • Recently issued on-the-run sovereign bond issued by a high-credit-quality government

   • Sovereign bond issued a year ago by a high-credit-quality government

   • High-credit-quality corporate bond

   • Low-credit-quality corporate bond

Alternatives to Direct Investment in Bonds

Because transacting in fixed-income securities may present challenges resulting from low liquidity in many segments of the fixed-income market, fund managers may use alternative methods to establish bond market exposures. The methods we outline are applicable across different fixed-income mandates. We will take a more in-depth look at the ones particularly relevant to passive and liability-driven mandates later as part of our coverage dedicated to such mandates. Next, we provide an overview of the most common methods—specifically, mutual funds, exchange-traded funds (ETFs), exchange-traded derivatives, and OTC derivatives. In considering direct versus indirect investments, the asset manager must weigh the ongoing fees associated with such instruments as mutual funds and ETFs against the bid–offer cost of direct investment in the underlying securities.

ETFs and mutual funds. These products provide an alternative to transacting in individual bonds. They are more liquid than the underlying securities. Mutual funds are pooled investment vehicles whose shares or units represent a proportional share in the ownership of the assets in an underlying portfolio. In the case of open-end mutual funds, new shares may be redeemed or issued at the fund’s net asset value (NAV) established at the end of each trading day based on the fund’s valuation of all existing assets minus liabilities, divided by the total number of shares outstanding. Bond mutual fund investors enjoy the advantage of being able to redeem holdings at the fund’s NAV rather than needing to sell illiquid positions. The benefit from economies of scale is usually the overriding factor for smaller investors in their choice of a bond mutual fund over direct investment. Because bonds often trade at a minimum lot size of USD1 million or higher per bond, successful replication of a broad index or construction of a diversified actively managed portfolio could easily require hundreds of millions of dollars in investments. Therefore, the greater diversification across fixed-income markets achievable by a larger fund may be well worth the additional cost in terms of an upfront load in some instances and an annual management fee.

Although investors benefit from increased diversification, the fund must outline its stated investment objectives and periodic fees, but actual security holdings are available only on a retroactive basis. Unlike the underlying securities, bond mutual funds have no maturity date; the fund manager continuously purchases and sells bonds to track index performance, and monthly interest payments fluctuate on the basis of fund holdings.

Exchange-traded funds share some mutual fund characteristics but have more tradability features. Investors benefit from greater bond ETF liquidity versus mutual funds given their availability to be purchased or sold throughout the trading day.

Exchange traded derivatives. Futures and options on futures provide exposure to underlying bonds. Being exchange traded, they involve financial instruments with standardized terms, documentation, and pricing traded on an organized exchange. Exchange-traded products also include interest rate products and options for interest rate–related ETFs.

OTC derivatives. Interest rate swaps are the most widely used OTC derivative worldwide and entail customized arrangements between two counterparties that reference an underlying market price or index. Some interest rate swaps are liquid, with multiple swap dealers posting competitive two-way quotes. In addition to interest rate swaps, fixed-income portfolio managers use inflation swaps, total return swaps, and credit swaps to alter their portfolio exposure. Because they trade over the counter, swaps may be tailored to an investor’s specific needs.

A total return swap (TRS), a common over-the-counter portfolio derivative strategy, combines elements of interest rate swaps and credit derivatives. Similar to an interest rate swap, a total return swap involves the periodic exchange of cash flows between two parties for the life of the contract. Unlike an interest rate swap, in which counterparties exchange a stream of fixed cash flows versus a floating-rate benchmark such as the MRR (the market reference rate) to transform fixed assets or liabilities to a variable exposure, a TRS has a periodic exchange based on a reference obligation that is an underlying equity, commodity, or bond index. Exhibit 9 outlines the most basic TRS structure. The total return receiver receives both the cash flows from the underlying index and any appreciation in the index over the period in exchange for paying the MRR plus a predetermined spread. The total return payer is responsible for paying the reference obligation cash flows and return to the receiver but will also be compensated by the receiver for any depreciation in the index or default losses incurred by the portfolio.

Exhibit 9:

Total Return Swap Mechanics

The TRS transaction is an over-the-counter derivative contract based on an ISDA (International Swaps and Derivatives Association) master agreement. This contract specifies a notional amount, periodic cash flows, and final maturity, as well as the credit and other legal provisions related to the transaction. The historical attractiveness of using TRS stemmed from the efficient risk transfer on the reference obligation from one counterparty to another on a confidential basis without requiring the full cash outlay associated with the mutual fund or ETF purchase. In fact, another way to think of the TRS is as a synthetic secured financing transaction in which the investor (the total return receiver) benefits from more-advantageous funding terms faced by a dealer (typically the total return payer) offering to facilitate the transaction.

The potential for both a smaller initial cash outlay and lower swap bid–offer costs compared with the transaction costs of direct purchase or use of a mutual fund or ETF are the most compelling reasons to consider a TRS to add fixed-income exposure.

That said, several considerations may offset these benefits in a number of instances:

• The investor does not legally own the underlying assets but, rather, has a combined synthetic long position in both the market and the credit risk of the index that is contingent on the performance of the total return payer. The total return receiver must both perform the necessary credit due diligence on its counterparty and face the rollover risk at maturity of having the ability to renew the contract with reasonable pricing and business terms in the future.

• Structural changes to the market and greater regulatory oversight, particularly capital rules affecting dealers, have raised the cost and increased the operational burden of these transactions because of the need to collateralize mark-to-market positions frequently and within shorter timeframe.

• As a funding cost arbitrage transaction, the TRS can allow investors to gain particular access to subsets of the fixed-income markets, such as bank loans or high-yield instruments for which cash markets are relatively illiquid or the cost and administrative complexity of maintaining a portfolio of these instruments is prohibitive for the investor.

A MODEL FOR FIXED-INCOME RETURNS

Learning Outcome

• describe and interpret a model for fixed-income returns

Investors often have views on future changes in the yield curve and structure or restructure their portfolios accordingly. Investment strategies should be evaluated in terms of expected returns rather than just yields to maturity.

A bond’s yield to maturity provides an incomplete measure of its expected return.

Instead, expected fixed-income returns consist of a number of different components in addition to yield to maturity.

Examining these components leads to a better understanding of the driving forces behind expected returns—on individual bonds and fixed-income portfolios.

The focus is on expected as opposed to realized returns, which may be decomposed in a similar manner.

Decomposing Expected Returns

Decomposing expected fixed-income returns allows an investor to differentiate among several important return components. At the most general level, expected returns, denoted as E(R), can be decomposed (approximately) in the following manner:

,where E(. . .) represents effects on expected returns based on expectations of the item in parentheses and Δ represents “change.” The decomposition holds only approximately and ignores taxes (note that some of the material on decomposing expected returns has been adapted from Hanke and Seals [2010]).

Coupon Income

Coupon income is the income that an investor receives from coupon payments relative to the bond’s price and interest on reinvestment income. Assuming there is no reinvestment income, coupon income equals a bond’s annual current yield.

Coupon income (or Current yield) = Annual coupon payment/Current bond price.

Rolldown Return

The rolldown return, sometimes referred to as “rolldown and carry return,” results from the bond “rolling down” the yield curve as the time to maturity decreases (see Exhibit 10), assuming zero interest rate volatility. Bond prices change as time passes even if the market discount rate remains the same. As time passes, a bond’s price typically moves closer to par. This price movement is illustrated by the constant-yield price trajectory, which shows the “pull to par” effect on the price of a bond trading at a premium or a discount to par value. If the issuer does not default, the price of a bond approaches par value as its time to maturity approaches zero.

Exhibit 10:

Rolling down the Yield Curve Effect

The rolldown return equals the bond’s percentage price change assuming an unchanged yield curve over the strategy horizon. Bonds trading at a premium to their par value will experience capital losses during their remaining life, and bonds trading at a discount relative to their par value will experience capital gains during their remaining life.

To compute the rolldown return, the bond has to be revalued at the end of the strategy horizon assuming an unchanged yield curve. Then the rolldown return is as follows:

The sum of the coupon income and the rolldown return may be referred to as the bond’s rolling yield.

Views of Benchmark Yields

The expected change in price based on investor’s views of benchmark yields to maturity and the term structure of yield volatility reflects an investor’s expectation of changes in yields to maturity and yield volatility over the investment horizon.

This expected change is zero if the investor expects yield curves and yield volatility to remain unchanged. Assuming the investor does expect a change in the yield curve, this expected return component is computed as follows:

where ModDur is the modified duration of a bond,

∆Yield is the expected change in yield to maturity, and Convexity reflects the second-order effect of the price–yield relationship.

Note that for bonds with embedded options, the duration and convexity measures used should be effective duration and effective convexity.

Also, in contrast to fixed-coupon bonds, floating-rate notes have a modified duration that is largely due to spread changes, as described in detail later.

Views of Yield Spreads

The expected change in price based on investor’s views of yield spreads reflects an investor’s expectation of changes in market credit spreads over the investment horizon.

When economic or credit conditions are improving, spreads are typically said to tighten, thereby reducing the required yield to maturity on the bond.

Deteriorating conditions would conversely result in higher required yields to maturity.

This component of expected return reflects general market conditions rather than any spread changes due to issuer-specific (or idiosyncratic) risk and is computed as follows:

Yield spreads can also fluctuate on the basis of idiosyncratic risk. Credit migration refers to credit quality changes that may result in an issuer downgrade or upgrade.

This can result in either lower spreads for higher ratings or higher spreads for lower ratings affecting the expected return on bonds.

Higher-quality credits tend to have low probabilities of default but can experience changes in bond prices due to an anticipated or actual migration.

The price impact is calculated in the same way as noted previously for market changes in yield to maturity. Note that investors face price declines on non-defaulted bonds if spreads widen. Yearly default rates can vary significantly and are more severe for speculative-grade (high-yield) issues.

Views of Currency Value Changes

If an investor holds bonds denominated in a currency other than her home currency, she also needs to factor in any expected fluctuations in the currency exchange rate or expected currency gains or losses over the investment horizon. The magnitude and direction of the change in the exchange rate can be based on a variety of factors, including the manager’s own view, results from surveys, or a quantitative model output. It can also be based on the exchange rate that can be locked in over the investment horizon using currency forwards.

Return measured in functional currency terms (domestic currency returns of foreign currency assets) can be shown as RDC = (1 + RFC)(1 + RFX) – 1 for a single asset or

for a portfolio, where RDC and RFC are the domestic and foreign currency returns expressed as a percentage, RFX is the percentage change of the domestic currency versus the foreign currency, and ωi is the respective portfolio weight of each foreign currency asset (in domestic currency terms), with the sum of ωi equal to 1. In the context of the return decomposition framework, RDC simply combines the third factor, E(ΔPrice due to investor’s view of benchmark yield), and the fifth factor, (+/– E(ΔFunctional currency value), in the expected fixed-income return model.

EXAMPLE 4

Decomposing Expected Returns

1. Ann Smith works for a US investment firm in its London office. She manages the firm’s British pound–denominated corporate bond portfolio. Her department head in New York City has asked Smith to make a presentation on next year’s total expected return of her portfolio in US dollars and the components of this return. Exhibit 11 shows information on the portfolio and Smith’s expectations for the next year. Expected return (for the bond portfolio) and its components are on an annualized basis, and any potential coupons are assumed to be paid annually. Calculate the total expected return of Smith’s bond portfolio, assuming no reinvestment income.

   Exhibit 11:

   Portfolio Characteristics and Expectations

   Notional principal of portfolio (in millions)	£100
   Average bond coupon payment (per £100 par value)	£2.75
   Coupon frequency	Annual
   Investment horizon	1 year
   Current average bond price	£97.12
   Expected average bond price in one year (assuming an unchanged yield curve)	£97.27
   Average bond convexity in one year	18
   Average bond modified duration in one year	3.70
   Expected average benchmark yield-to-maturity change	0.26%
   Expected change in spread (spread expected to narrow in this scenario)	-0.10%
   Expected currency losses (£ depreciation versus US$)	0.50%

   Solution:

   The portfolio’s coupon income is 2.83%. The portfolio has an average coupon of £2.75 on a £100 notional principal and currently trades at £97.12. The coupon income over a one-year horizon is 2.83% = £2.75/£97.12.

   In one year’s time, assuming an unchanged yield curve and zero interest rate volatility, the rolldown return is 0.17% = (£97.27 – £97.12)/£97.12.

   The rolling yield, which is the sum of the coupon income and the rolldown return, is 3.00% = 2.83% + 0.17%.

   The expected change in price based on Smith’s views of benchmark yields to maturity is –0.96%, calculated as follows: The bond portfolio has a modified duration of 3.70 and a convexity statistic of 18. Smith expects an average benchmark yield-to-maturity change of 0.26%. Smith expects to incur a decrease in prices and a reduction in return based on her rate view. The expected change in price based on Smith’s views of yields to maturity and yield spreads is thus –0.0096 = (–3.70 × 0.0026) + [½ × 18 × (0.0026)2]. So the expected reduction in return based on Smith’s rate view is 0.96%.

   Smith expects an impact from the 0.1% change (narrowing in this scenario) in spread in her well-diversified investment-grade bond portfolio. The impact on the expected return is, therefore, 0.37% = [–3.70 × (–0.0010)] + [1/2 × 18 × (–0.0010)2].

   Smith expects the British pound, the foreign currency in which her bond position is denominated, to depreciate by an annualized 50 bps (or 0.5%) over the investment horizon against the US dollar, the home country currency. The expected currency loss to the portfolio is thus 0.50%.

   The total expected return on Smith’s bond position is 1.91%, as summarized in Exhibit 12.

   Exhibit 12:

   Return Component Calculations

   Return Component	Formula	Calculation
   Coupon income	Annual coupon payment/Current bond price	£2.75/£97.12 = 2.83%
   + Rolldown return	$(Bond priceEnd−of−horizon period−Bond priceBeginning−of−horizon period)Bond priceBeginning−of−horizon period$(Bond price𝐸𝑛𝑑-𝑜𝑓-ℎ𝑜𝑟𝑖𝑧𝑜𝑛 𝑝𝑒𝑟𝑖𝑜𝑑−Bond price𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔-𝑜𝑓-ℎ𝑜𝑟𝑖𝑧𝑜𝑛 𝑝𝑒𝑟𝑖𝑜𝑑)Bond price𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔-𝑜𝑓-ℎ𝑜𝑟𝑖𝑧𝑜𝑛 𝑝𝑒𝑟𝑖𝑜𝑑	(£97.27 – £97.12)/£97.12 = 0.17%
   = Rolling yield	Coupon income + Rolldown return	2.83% + 0.17% = 3.00%
   +/– E(ΔPrice* based on Smith’s benchmark yield view)	(−ModDur × ∆Yield) + [½ × Convexity × (∆Yield)2]	(−3.70 × 0.0026) + [½ × 18 × (0.0026)2] = –0.96%
   +/– E(ΔPrice due to investor’s view of yield spreads)	(−ModDur × ∆Spread) + [½ × Convexity × (∆Spread)2]	(–3.70 × –0.0010) + [1/2 × 18 × (–0.0010)2] = 0.37%
   +/– E(Currency gains or losses)	Given	–0.50%
   = Total expected return		1.91%

   *Note that the change in price in the context of this example refers to the change in portfolio value.

Estimation of the Inputs

In the model for fixed-income returns discussed earlier, some of the individual expected return components can be more easily estimated than others. The easiest component to estimate is the coupon income. The return model’s most uncertain individual components are the investor’s views of changes in benchmark yields and yield spreads and expected currency movements. These components are normally based on purely qualitative (subjective) criteria, a quantitative model (including surveys), or a mixture of the two. Although a quantitative approach may seem more objective, there are a number of quantitative models that can be used, each with different methodologies associated with the underlying calculations.

Limitations of the Expected Return Decomposition

The return decomposition just described is an approximation; only duration and convexity are used to summarize the price–yield relationship. In addition, the model implicitly assumes that all intermediate cash flows of the bond are reinvested at the yield to maturity, which results in different coupon reinvestment rates for different bonds.

The model also ignores other factors, such as local richness/cheapness effects and potential financing advantages. Local richness/cheapness effects are deviations of individual maturity segments from the fitted yield curve, which was obtained using a curve estimation technique. Yield curve estimation techniques produce relatively smooth curves, and there are likely slight deviations from the curve in practice. There may be financing advantages to certain maturity segments in the repo market. The repo market provides a form of short-term borrowing for dealers in government securities who sell government bonds to other market participants overnight and buy them back, typically on the following day. In most cases, local richness/cheapness effects and financing advantages tend to be relatively small and are thus not included in the expected return decomposition model.

EXAMPLE 5

Components of Expected Return

1. Kevin Tucker manages a global bond portfolio. At a recent investment committee meeting, Tucker discussed his portfolio’s domestic (very high-credit-quality) government bond allocation with another committee member. The other committee member argued that if the yield curve is expected to remain unchanged, the only determinants of a domestic government bond’s expected return are its coupon payment and its price.

   Explain why the other committee member is incorrect, including a description of the additional expected return components that need to be included.

   Solution:

   A bond’s coupon payment and its price allow only its coupon income to be computed. Coupon income is an incomplete measure of a bond’s expected return. For domestic government bonds, in addition to coupon income, the rolldown return needs to be considered. The rolldown return results from the fact that bonds are pulled to par as the time to maturity decreases, even if the yield curve is expected to remain unchanged over the investment horizon. Currency gains and losses would also need to be considered in a global portfolio. Because the portfolio consists of government bonds with very high credit quality, the view on yield spreads is less relevant for Tucker’s analysis. For government and corporate bonds with lower credit quality, however, yield spreads would also need to be considered as additional return components.

LEVERAGE

Learning Outcome

• discuss the use of leverage, alternative methods for leveraging, and risks that leverage creates in fixed-income portfolios

Leverage is the use of borrowed capital to increase the magnitude of portfolio positions, and it is an important tool for fixed-income portfolio managers.

By using leverage, fixed-income portfolio managers may be able to increase portfolio returns relative to what they can achieve in unleveraged portfolios.

Managers often have mandates that place limits on the types of securities they may hold.

Simultaneously, managers may have return objectives that are difficult to achieve, especially during low–interest rate environments.

Through the use of leverage, a manager can increase his investment exposure and may be able to increase the returns to fixed-income asset classes that typically have low returns.

The increased return potential, however, comes at the cost of increased risk: If losses occur, these would be higher than in unleveraged positions.

Using Leverage

Leverage increases portfolio returns if the securities in the portfolio have returns higher than the cost of borrowing.

In an unleveraged portfolio, the return on the portfolio (rp) equals the return on invested funds (rI).

When the manager uses leverage, however, the invested funds exceed the portfolio’s equity by the amount that is borrowed.

The leveraged portfolio return, rp, can be expressed as the total investment gains per unit of invested capital:

where

VE = Value of the portfolio’s equity

VB = Borrowed funds

rB = Borrowing rate (cost of borrowing)

rI = Return on the invested funds (investment returns)

rp = Return on the levered portfolio

The numerator represents the total return on the portfolio assets, rI × (VE + VB), minus the cost of borrowing, VB × rB, divided by the portfolio’s equity.

The leveraged portfolio return can be decomposed further to better identify the effect of leverage on returns:

This expression decomposes the leveraged portfolio return into the return on invested funds and a portion that accounts for the effect of leverage.

If rI > rB, then the second term is positive because the rate of return on invested funds exceeds the borrowing rate; in this case, leverage increases the portfolio’s return.

If rI < rB, then the second term is negative because the rate of return on invested funds is less than the borrowing rate; in this case, the use of leverage decreases the portfolio’s return.

The degree to which the leverage increases or decreases portfolio returns is proportional to the use of leverage (amount borrowed), VB/VE, and the amount by which investment return differs from the cost of borrowing, rI – rB.

Methods for Leveraging Fixed-Income Portfolios

Fixed-income portfolio managers have a variety of tools available to create leveraged portfolio exposures—notably, the use of financial derivatives and borrowing via collateralized money markets. Derivatives and borrowing are explicit forms of leverage. Other forms of leverage, such as the use of structured financial instruments, are more implicit. We provide a description of the most common ones.

Futures Contracts

Futures contracts embed significant leverage because they permit the counterparties to gain exposure to a large quantity of the underlying asset without having to actually transact in the underlying.

Futures contracts can be obtained for a modest investment that comes in the form of a margin deposit.

A futures contract’s notional value equals the current value of the underlying asset multiplied by the multiplier, or the quantity of the underlying asset controlled by the contract.

The futures leverage is the ratio of the futures exposure (in excess of the margin deposit) normalized by the amount of margin required to control the notional amount.

We can calculate the futures leverage using the following equation:

Swap Agreements ✅

An interest rate swap can be viewed as a portfolio of bonds.

In an interest rate swap, the fixed-rate payer is effectively short a fixed-rate bond and long a floating-rate bond.

When interest rates increase, the value of the swap to the fixed-rate payer increases because the present value of the fixed-rate liability decreases and the floating-rate payments received increase.

The fixed-rate receiver in the interest rate swap agreement effectively has a long position in a fixed-rate bond and a short position in a floating-rate bond.

If interest rates decline, the value of the swap to the fixed-rate receiver increases because the present value of the fixed-rate asset increases and the floating-rate payments made decrease.

Because interest rate swaps are economically equivalent to a long–short bond portfolio, they provide leveraged exposure to bonds; the only capital required to enter into swap agreements is collateral required by the counterparties. ´🟠

Collateral for interest rate swap agreements has historically occurred between the two (or more) counterparties in the transaction. Increasingly, collateral for interest rate and other swaps occurs through central clearinghouses.

Repurchase Agreements

Repurchase agreements (repos) are an important source of short-term financing for fixed-income security dealers and other financial institutions, as evidenced by the trillions of dollars of repo transactions that take place annually.

In a repurchase agreement, a security owner agrees to sell a security for a specific cash amount while simultaneously agreeing to repurchase the security at a specified future date (typically one day later) and price. 📍

Repos are thus effectively collateralized loans. 💡

When discussing a repo, the transaction normally refers to the borrower’s standpoint; from the standpoint of the lender (such as a money market fund), these agreements are referred to as reverse repos. Exhibit 13 illustrates the transaction.

The interest rate on a repurchase agreement, called the repo rate, is the difference between the security’s selling price and its repurchase price.

For example, consider a dealer wishing to finance a EUR15 million bond position with a repurchase agreement.

The dealer enters into an overnight repo at a repo rate of 5%. We can compute the price at which she agrees to repurchase this bond after one day as the EUR15 million value today plus one day of interest. The interest amount is computed as follows:

Dollar interest = Principal amount × Repo rate × (Term of repo in days/360) ⭐️

Continuing with the example, the dollar interest is EUR2,083.33 = EUR15 million × 5% × (1/360). Thus, the dealer will repurchase the bond the next day for EUR15,002,083.33.

Exhibit 13:

Repo and Reverse Repo

The term, or length, of a repurchase agreement is measured in days.

Overnight repos are common, although they are often rolled over to create longer-term funding.

A repo agreement may be cash driven or security driven.

Cash-driven transactions feature one party that owns bonds and wants to borrow cash, as in the foregoing example. Cash-driven transactions usually feature “general collateral”—securities commonly accepted by investors and dealers, such as Treasury bonds. 💡💡

In a security-driven transaction, the lender typically seeks a particular security. The motives may be for hedging, arbitrage, or speculation.💡

Credit risk is a concern in a repo agreement, in particular for the counterparty that lends capital.

Protection against a default by the borrower is provided by the underlying collateral bonds.

Additional credit protection comes from the “haircut,” the amount by which the collateral’s value exceeds the repo principal amount. 📍

For example, haircuts for high-quality government bonds typically range from 1% to 3% and are higher for other types of bonds. 🐤

The size of the haircut serves to not only protect the lender against a potential default by the borrower but also to limit the borrower’s net leverage capacity. 💡

Generally, the size of the haircut increases as the price volatility of the underlying collateral increases.💡

Repos are categorized as bilateral repos or tri-party repos, depending on the way they are settled. 💡

Bilateral repos are conducted directly between two institutions, and settlement is typically conducted as “delivery versus payment,” meaning that the exchanges of cash and collateral occur simultaneously through a central custodian (for example, the Depository Trust Company in the United States). 📍

Bilateral repos are usually used for security-driven transactions.

Tri-party repo transactions involve a third party that provides settlement and collateral management services. 📍

Most cash-motivated repo transactions against general collateral are conducted as tri-party repo transactions.

Security Lending

Security lending is another form of collateralized lending and is closely linked to the repo market. 📍

The primary motive of security lending transactions is to facilitate short sales, which involve the sale of securities the seller does not own. 💡

A short seller must borrow the securities he has sold short in order to deliver them upon trade settlement.

Another motive for security lending transactions is financing, or collateralized borrowing. In a financing-motivated security loan, a bond owner lends the bond to another investor in exchange for cash.💡

Security lending transactions are collateralized by cash or high-credit-quality bonds.

In the United States, most transactions feature cash collateral, although in many other countries, highly rated bonds are used as collateral. Typically, security lenders require collateral valued in excess of the value of the borrowed securities when bonds are used as collateral.

For example, if high-quality government bonds are used as collateral, the lender may require bonds valued at 102% of the value of the borrowed securities. The extra 2% functions in the same way as the haircut in the repo market, providing extra protection against borrower default. The collateral required will increase if lower-quality bonds are used as collateral.

In security lending transactions with cash collateral, the security borrower typically pays the security lender, typically a long-only investment fund, a fee equal to a percentage of the value of the securities loaned. For securities that are readily available for lending, that fee is small. The security lender earns an additional return by reinvesting the cash collateral. In cases where the security loan is initiated for financing purposes, the lending fee is typically negative, indicating that the security lender pays the security borrower a fee in exchange for its use of the cash.

When bonds are posted as collateral, the income earned on the collateral usually exceeds the security lending rate; the security lender (who is in possession of the bonds as collateral) usually repays the security borrower a portion of the interest earned on the bond collateral. The term rebate rate refers to the portion of the collateral earnings rate that is repaid to the security borrower by the security lender. This relationship can be expressed as follows:

Rebate rate = Collateral earnings rate – Security lending rate. ⭐️

When securities are difficult to borrow, typically because there is high demand to short those securities, the rebate rate may be negative, which means the fee for borrowing the securities is greater than the return earned on the collateral. In this case, the security borrower pays a fee to the security lender in addition to forgoing the interest earned on the collateral.

There are important differences between repurchase agreements and security lending transactions. Unlike repurchase agreements, security lending transactions are typically open-ended. The security lender may recall the securities at any time, forcing the borrower to deliver the bonds by buying them back or borrowing from another lender. Similarly, the borrower may deliver the borrowed securities back to the lender at any time, forcing the lender, or its agent, to return the collateral (cash or bonds) and search for another borrower.

Risks of Leverage

Leverage alters the risk–return properties of an investment portfolio. A heavily leveraged portfolio may incur significant losses even when portfolio assets suffer only moderate valuation declines.

Leverage can lead to forced liquidations. If the value of the portfolio decreases, the portfolio’s equity relative to borrowing levels is reduced and the portfolio’s leverage increases. Portfolio assets may be sold in order to pay off borrowing and reduce leverage.

If portfolio assets are not liquidated, then the overall leverage increases, corresponding to higher levels of risk. Decreases in portfolio value can lead to forced liquidations even if market conditions are unfavorable for selling—for example, during crisis periods.

The term “fire sale” refers to forced liquidations at prices that are below fair value as a result of the seller’s need for immediate liquidation. Reducing leverage, declining asset values, and forced sales have the potential to create spiraling effects that can result in severe declines in values and reduction in market liquidity.

Additionally, reassessments of counterparty risk typically occur during extreme market conditions, such as during the 2008–09 financial crisis. During periods of financial crisis, counterparties to short-term financing arrangements, such as credit lines, repurchase agreements, and security lending agreements, may withdraw their financing. These withdrawals undermine the ability of leveraged market participants to maintain their investment exposures. Thus, leveraged investors may be forced to reduce their investment exposure at exactly the worst time—that is, when prices are depressed.

EXAMPLE 6

Using Leverage in a Fixed-Income Portfolio

Arturo manages a mutual fund that is benchmarked to the Global Aggregate Bond Index.

He currently has a bullish view of the global economy and believes corporate bond spreads are attractive.

He is bearish on US Treasury interest rates given his economic growth forecast and expects rates to increase.

The fund’s US corporate bond holdings have a duration of seven years.

He believes the best opportunities are in emerging market securities, and in particular, he is bullish on Brazilian rates, expecting them to decrease.

The fund has experienced strong inflows recently and is fully invested.

Arturo is evaluating tools to potentially increase the fund’s total return by creating leveraged fixed-income exposures.

Given Arturo’s plan to leverage exposures in his fund, discuss how he would achieve his objectives and identify the strategy risks.

Solution:

The mutual fund is fully invested and, therefore, Arturo needs to use leverage to potentially increase his returns.

His bearish view on US Treasury interest rates would require that he reduce the fund’s seven-year duration contributed by the US corporate bond holdings.

He can sell the number of futures contracts on US Treasuries whose notional value and associated duration would offset the duration of the corporate bonds to his new target duration.

Doing so would allow him to retain exposure (spread duration) to the corporate bonds whose spreads may contract as the economy grows while shedding the interest rate exposure, since he believes rates will rise, adversely affecting bond prices.

Arturo’s bullish view on Brazilian rates can be expressed by entering into a receive fixed-rate, pay floating-rate swap on Brazilian rates. The fund will effectively have the equivalent of a fixed-rate bond that will appreciate in price if his view materializes and Brazilian interest rates fall.

Both the short US Treasury futures and long Brazilian interest rate swap positions are leveraged since the only capital used is the collateral required by the counterparties. The risk to the leveraged strategy is that if Arturo’s view on either position turns out to be incorrect, losses are magnified. This may also require positions to be closed and assets sold to cover the losses, which may occur at an inopportune time if the markets have sold off.

FIXED-INCOME PORTFOLIO TAXATION

https://study.cfainstitute.org/app/cfa-institute-program-level-iii-for-august-2024#read/study_task/2563243/fixed-income-portfolio-taxation-1

Learning Outcome

• discuss differences in managing fixed-income portfolios for taxable and tax-exempt investors

A tax-exempt investor’s objective is to achieve the highest possible risk-adjusted returns net of fees and transaction costs. A prudent taxable investor needs to also consider the effects of taxes on both expected and realized net investment returns.

The investment management industry has traditionally made investment decisions based on pretax returns as though investors are tax exempt (such as pension funds in many countries; see Rogers [2006]). The majority of the world’s investable assets, however, are owned by taxable investors, who are concerned with after-tax, rather than pretax, returns.

Taxes may differ among investor types, among countries, and on the basis of income source, such as interest or capital gains. In many countries, pension funds are exempt from taxes but corporations generally have to pay tax on their investments. Many countries make some allowance for tax-sheltered investments that individuals can use (up to certain limits). These types of tax shelters generally offer either an exemption from tax on investment income or a deferral of taxes until an investor draws money from the shelter (usually after retirement). Such shelters allow returns to accrue on a pretax basis until retirement, which can provide substantial benefits. In a fixed-income context for taxable investors, coupon payments (interest income) are typically taxed at the investor’s normal income tax rate. Capital gains, however, may be taxed at a lower effective rate than an investor’s normal income tax rate. In some countries, income from special types of fixed-income securities, such as bonds issued by a sovereign government, a non-sovereign government, or various government agencies, may be taxed at a lower effective rate or even not taxed.

Specific tax rules vary among jurisdictions. Any discussion of the effect of taxes on investor returns—and, therefore, on how portfolios should optimally be managed for taxable investors—is especially challenging if it needs to apply on a global level. Although accounting standards have become more harmonized globally, any kind of tax harmonization among countries is not likely to occur anytime soon. An investor should consider how taxes affect investment income in the country where the income is earned and how the investment income is treated when it is repatriated to the investor’s home country. Treaties between countries may affect tax treatment of investment income. Taxes are complicated and can make investment decisions difficult. Portfolio managers who manage assets for taxable individual investors, as opposed to tax-exempt investors, need to consider a number of issues.

Principles of Fixed-Income Taxation

Although tax codes differ among jurisdictions, there are certain principles that most tax codes have in common with regard to taxation of fixed-income investments:

• The two primary sources of investment income that affect taxes for fixed-income securities are coupon payments (interest income) and capital gains or losses.

• In general, tax is payable only on capital gains and interest income that have actually been received. In some countries, an exception to this rule applies to zero-coupon bonds. Imputed interest that is taxed throughout a zero-coupon bond’s life may be calculated. This method of taxation ensures that tax is paid over the bond’s life and that the return on a zero-coupon bond is not taxed entirely as a capital gain.

• Capital gains are frequently taxed at a lower effective tax rate than interest income.

• Capital losses generally cannot be used to reduce sources of income other than capital gains. Capital losses reduce capital gains in the tax year in which they occur. If capital losses exceed capital gains in the year, they can often be “carried forward” and applied to gains in future years; in some countries, losses may also be “carried back” to reduce capital gains taxes paid in prior years. Limits on the number of years that capital losses can be carried forward or back typically exist.

• In some countries, short-term capital gains are taxed at a different (usually higher) rate than long-term capital gains.

An investor or portfolio manager generally has no control over the timing of when coupon income is received and the related income tax must be paid. However, he or she can generally decide the timing of the sale of investments and, therefore, has some control over the timing of realized capital gains and losses. This control can be valuable for a taxable investor because it may be optimal to delay realizing gains and related tax payments and to realize losses as early as possible. This type of tax-driven strategic behavior is referred to as tax-loss harvesting.

Key points for managing taxable fixed-income portfolios include the following:

• Selectively offset capital gains and losses for tax purposes.

• If short-term capital gains tax rates are higher than long-term capital gains tax rates, then be judicious when realizing short-term gains.

• Realize losses taking into account tax consequences. They may be used to offset current or future capital gains for tax purposes.

• Control turnover in the fund. In general, the lower the turnover, the longer capital gains tax payments can be deferred.

• Consider the trade-off between capital gains and income for tax purposes.

Investment Vehicles and Taxes

The choice of investment vehicle often affects how investments are taxed at the final investor level. In a pooled investment vehicle (sometimes referred to as a collective investment scheme), such as a mutual fund, interest income is generally taxed at the final investor level when it occurs—regardless of whether the fund reinvests interest income or pays it out to investors. In other words, for tax purposes the fund is considered to have distributed interest income for tax purposes in the year it is received even if it does not actually pay it out to investors. Taxation of capital gains arising from the individual investments within a fund is often treated differently in different countries.

Some countries, such as the United States, use what is known as pass-through treatment of capital gains in mutual funds. Realized net capital gains in the underlying securities of a fund are treated as if distributed to investors in the year that they arise, and investors need to include the gains on their tax returns. Other countries, such as the United Kingdom, do not use pass-through treatment. Realized capital gains arising within a fund increase the net asset value of the fund shares that investors hold. Investors pay taxes on the net capital gain when they sell their fund shares. This tax treatment leads to a deferral in capital gains tax payments. A UK portfolio manager’s decisions on when to realize capital gains or losses do not affect the timing of tax payments on capital gains by investors.

In a separately managed account, an investor typically pays tax on realized gains in the underlying securities at the time they occur. The investor holds the securities directly rather than through shares in a fund. For separately managed accounts, the portfolio manager needs to consider tax consequences for the investor when making investment decisions.

Tax-loss harvesting, which we defined earlier as deferring the realization of gains and realizing capital losses early, allows investors to accumulate gains on a pretax basis. The deferral of taxes increases the present value of investments for the investor.

EXAMPLE 7

Managing Taxable and Tax-Exempt Portfolios

A bond portfolio manager needs to raise €10,000,000 in cash to cover outflows in the portfolio she manages. To satisfy her cash demands, she considers one of two corporate bond positions for potential liquidation: Position A and Position B. For tax purposes, capital gains receive pass-through treatment; realized net capital gains in the underlying securities of a fund are treated as if distributed to investors in the year that they arise. Assume that the capital gains tax rate is 28% and the income tax rate for interest is 45%. Exhibit 14 provides relevant data for the two bond positions.

Exhibit 14:

Selected Data for Two Bonds

	Position A	Position B
Current market value	€10,000,000	€10,000,000
Capital gain/loss	€1,000,000	–€1,000,000
Coupon rate	5.00%	5.00%
Remaining maturity	10 years	10 years
Income tax rate	45%
Capital gains tax rate	28%

The portfolio manager considers Position A to be slightly overvalued and Position B to be slightly undervalued. Assume that the two bond positions are identical with regard to all other relevant characteristics. How should the portfolio manager optimally liquidate bond positions if she manages the portfolio for:

1. tax-exempt investors?

   Solution to 1:

   The taxation of capital gains and capital losses has minimal consequences for tax-exempt investors. Consistent with the portfolio manager’s investment views, the portfolio manager would likely liquidate Position A, which she considers slightly overvalued, rather than liquidating Position B, which she considers slightly undervalued.

2. taxable investors?

   Solution to 2:

   All else equal, portfolio managers for taxable investors should have an incentive to defer capital gains taxes and realize capital losses early (tax-loss harvesting) so that losses can be used to offset current or future capital gains. Despite the slight undervaluation of the position, the portfolio manager might want to liquidate Position B because of its embedded capital loss, which will result in a lower realized net capital gain being distributed to investors. This decision is based on the assumption that there are no other capital losses in the portfolio that can be used to offset other capital gains. Despite the slight overvaluation of Position A, its liquidation would be less desirable for a taxable investor because of the required capital gains tax.

SUMMARY

• Fixed-income investments provide diversification benefits in a portfolio context. These benefits arise from the generally low correlations of fixed-income investments with other major asset classes, such as equities. ✅

• Floating-rate and inflation-linked bonds can be used to hedge inflation risk. ✅

• Fixed-income investments have regular cash flows, which is beneficial for the purposes of funding future liabilities. ✅

• For liability-based fixed-income mandates, portfolio construction follows two main approaches—cash flow matching and duration matching—to match fixed-income assets with future liabilities. 💡

• Total return mandates are generally structured to either track or outperform a benchmark. ✅

• Total return mandates can be classified into various approaches according to their target active return and active risk levels. Approaches range from pure indexing to enhanced indexing to active management. 💡

• Bond Portfolio Duration is the sensitivity of a portfolio of bonds to small changes in interest rates. It can be calculated as the weighted average of time to receipt of the aggregate cash flows or, more commonly, as the weighted average of the individual bond durations that comprise the portfolio. 💡

• Modified Duration of a Bond Portfolio indicates the percentage change in the market value given a change in yield-to-maturity. Modified duration of a portfolio comprising j fixed income securities can be estimated as💡

  $AvgModDur=∑j=1JModDurj(MVjMV)$

where MV stands for market value of the portfolio and MVj is the market value of a specific bond.

• Convexity of a bond portfolio is a second-order effect; it operates behind duration in importance and can largely be ignored for small yield changes. When convexity is added with the use of derivatives, however, it can be extremely important to returns.💡

• Effective duration and convexity of a portfolio are the relevant summary statistics when future cash flows of bonds in a portfolio are contingent on interest rate changes. 💡

• Spread duration is a useful measure for determining a portfolio’s sensitivity to changes in credit spreads. It provides the approximate percentage increase (decrease) in bond price expected for a 1% decrease (increase) in credit spread. 💡

• Duration times spread is a modification of the spread duration definition to incorporate the empirical observation that spread changes across the credit spectrum tend to occur on a proportional percentage basis rather than being based on absolute basis point changes. 🟠

• Portfolio dispersion captures the variance of the times to receipt of cash flows around the duration. It is used in measuring interest rate immunization for liabilities. 💡

• Duration management is the primary tool used by fixed-income portfolio managers. ✅

• Convexity supplements duration as a measure of a bond’s price sensitivity for larger movements in interest rates. Adjusting convexity can be an important portfolio management tool. 🟠

• For two portfolios with the same duration, the portfolio with higher convexity has higher sensitivity to large declines in yields to maturity and lower sensitivity to large increases in yields to maturity. 💡

• Interest rate derivatives can be used effectively to increase or decrease duration and convexity in a bond portfolio. ✅

• Liquidity is an important consideration in fixed-income portfolio management. Bonds are generally less liquid than equities, and liquidity varies greatly across sectors. ✅

• Liquidity affects pricing in fixed-income markets because many bonds either do not trade or trade infrequently.✅

• Liquidity affects portfolio construction because there is a trade-off between liquidity and yield to maturity. 💡 Less liquid bonds have higher yields to maturity, all else being equal, and may be more desirable for buy-and-hold investors. Investors anticipating liquidity needs may forgo higher yields to maturity for more liquid bonds.

• Investors can obtain exposure to the bond market using mutual funds and ETFs that track a bond index. Shares in mutual funds are redeemable at the net asset value with a one-day time lag. ETF shares have the advantage of trading on an exchange. ✅

• A total return swap, an over-the-counter derivative, allows an institutional investor to transform an asset or liability from one asset category to another—for instance, from variable-rate cash flows referencing the market reference rate to the total return on a particular bond index. ✅

• A total return swap can have some advantages over a direct investment in a bond mutual fund or ETF. As a derivative, it requires less initial cash outlay than direct investment in the bond portfolio for similar performance but carries counterparty risk. 💡

• As a customized over-the-counter product, a TRS can offer exposure to assets that are difficult to access directly, such as some high-yield and commercial loan investments. ✅

• When evaluating fixed-income investment strategies, it is important to consider expected returns and to understand the various components of expected returns. ✅

• Decomposing expected fixed-income returns allows investors to understand the different sources of returns given expected changes in bond market conditions. ✅

• A model for expected fixed-income returns can decompose them into the following components: coupon income, rolldown return, expected change in price based on investor’s views of yields to maturity and yield spreads, and expected currency gains or losses. 💡

• Leverage is the use of borrowed capital to increase the magnitude of portfolio positions. By using leverage, fixed-income portfolio managers may be able to increase portfolio returns relative to what they can achieve in unleveraged portfolios. The potential for increased returns, however, comes with increased risk. ✅

• Methods for leveraging fixed-income portfolios include the use of futures contracts, swap agreements, repurchase agreements, structured financial instruments, and security lending. 💡

• Taxes can complicate investment decisions in fixed-income portfolio management. Complications result from the differences in taxation among investor types, countries, and income sources. ✅

• The two primary sources of investment income that affect taxes for fixed-income securities are coupon payments (interest income) and capital gains or losses. Tax is usually payable only on capital gains and interest income that have actually been received. ✅

• Capital gains are frequently taxed at a lower effective tax rate than interest income. If capital losses exceed capital gains in the year, they can often be “carried forward” and applied to gains in future years. 💡